If series Sum(an) and Sum(bn) with positive terms are convergent, is the series Sum(an*bn) converegent? Note: 1. Sum replaces the symbol for summation 2. an and bn are nth elements of the two series
The formula for the loan one can get with a payment of $P paying monthly for 15 years at an interest rate of r is: L=(12P/r)[1-(1+(r/12))^(-180)] a.) Find dL/dt, the rate of change of the loan with respect to time. (Here, t is the time that is passing, not the t in the original function if you know the loan. Trea
A leaking oil tank has a capacity of 500 000 liters of oil. The rate of leakage depends on the pressure of oil remaining in the tank and the pressure depends on the height of oil. When the tank is half-full, it loses 20L/min. How long goes it take to lose 15 000L from half-full?
Please see the attached problem file
Explaination for derivatives related to exponential and logarithmic functions ,formulae used to solve them and solutions to some problems. All problems are in the solution file
Hello, What is the equation of three bisecting solid rods centered at the origin? Given 3 solid rods of length 3 and diameter 1. One rod is on the x-axis One rod is on the y-axis and One rod is on the z-axis Each is centered at the origin and is perpendicular to the other rods in each axis. Need equation in rectan
The key is whether or not you are plugging the result of a function into another function. The idea is shown by contrasting the procedures for taking the derivatives of sin(x^2) and x^2*sin(x).
Eggs are produced at a rate of R(t)eggs per hour,where t=0 represents 12:00 midnight and R(t)(in thousands of eggs) is :- R(t)= -10cospi/12t+10 a)how many eggs are produced in one day. b)When are the eggs produced at the fastest rate c)A machine can produce eggs at a constant rate. At the end of 1 week the same
Compute the distance from a point b = (1, 0, 0, 1)^T to a line which passes through two points (0, 1, 1, 0)^T and (0, 1, 0, 2)^T. Here ^T denotes the operation of transposition, i.e. the points are represented by column-vectors instead of row-vectors.
Xy' + (1+x)y = 3 with y(4) = 50
Y' = (x+2)^2e^y with y(1) = 0
Northbound ship A leaves the harbour at 10:00 with a speed of 12km/h. Westbound ship B leaves the same harbour at 10:30 with a speed of 16km/h. (a) How fast are the ships separating at 11:30? (b) When is their rate of separation 18.86 km/h
What did I do wrong? 1. Find f'(x) when f(x)= 5x(sinx + cosx) My answer: cos(4x^2)- sin(6x^2)/(5x^2) 2. Find f'(x) when f(x)= ((x^3) + 4x + 4))^2 My answer: 6x^2(x^3 + 4x + 4) 3. Find f'(x) when f(x)= (3x + 8)^-3 My answer: -6(3x + 8) 4. Find f'(x) when f(x)= Sq root of (5x + 8) My answer: x/5x + 8 5. Find f'(x) when f(
Find the surface area of the solid that is the intersection of the two solid cylinders: x^2 + z^2 <= k^2 (x squared plus z squared is less than or equal to a constant squared) AND x^2 + y^2 <= k^2 (x squared plus y squared is less than or equal to the same constant squared) What is my f(x,y)? What are my limits of integr
Find intervals on which the function is: (a) increasing (b) decreasing (c) concave up (d) concave down find any (e) local extreme values and (f) inflection points for the equation y = x to the 4/5 power times(2-x)
Let f be the function defined by f(x)=sin squared x - sinx for 0<or=x<or=(3pi)over 2. a. find the x- intercepts of the graph of f b.find the intervals on which f is increasing c. find the absolute maximum and absolute minimum value of f. Justify your answer.
The parabola y = (x^2) + 3 has two tangents which pass through the point (0, -2). One is tangent to the to the parabola at (A, A^2 + 3) and the other at (-A, A^2 + 3). Find (the positive number) ? If a ball is thrown vertically upward from the roof of 64ft foot building with a velocity of 96 ft/sec, its height after t seconds
Find the derivative of: f(x) = sqaure roo 4 / t^3 f(x) = 5 + 2/x + 4/x^2 f(x) = ((4x^3) - 2)/ x^4
Let g(x) = 300-8x^3-x^4 -Find the local maximum and minimum values. -Find the intervals of concavity and the inflection points. -Use this information to carefully sketch the graph of g.
Find dy/dx by implicit differentiation of the following: x^4-y^4-x+y=10 x^3y^3-x^2y^2+y=19 Any help would be appreciated! Thank you
Ichiro hits the ball and runs toward first base with a speed of 25 feet per second. The shortstop, who is exactly 40 feet in from third base on the baseline, gets the ball exactly 1.7 seconds after Ichiro started running (assume he runs at a constant rate.) At what rate is Ichiro's distance to the shortstop increasing at the m
A series of swells passes through a group of surfers. They notice that for a few minutes, the waves pass through at regular intervals: every 14 seconds. Let t=0 be the time when the wave is at its lowest point. The maximum instantaneous increase in height of the wave is 2.25 feet per second. a. Find r(t), the rate of chang
Find the sum: 1/8+1/4+1/2+1+........64
What is the square root of the ln of x?
What are Gerhard Gentzen's mathematical accomplishments?
Prove that the point p is a limit point of the point set X if and only if each open point set containing p contains a point in X which is different from p. Prove without using sequences. Only use the def. of open set, open interval, and that the point p is a limit point of the point set X means that each open interval containing
A movie theater has a screen that is positioned 10 feet off the floor and is 25 feet high. The first row of seats is placed 9 feet from the screen and the rows are 3 feet apart. The floor of the seating area is inclined at an angle above the horizontal and the distance up the incline that you sit is x. The theater has 21 ro
1) The area of a circle is decreasing at the rate of 2 pie cm^2/s. At what rate is the radius of the circle decreasing when its area is 75 pie cm^2? 2)Find f'(-1), given f(y)=h(g(y)), h(2)=55, g(-1)=2, h'(2)=-1, and g'(-1)=7
Solve (1-x^2)^(1/2)y'+1+y^2=0 xy(1+x^2)y'-(1+y^2)=0 xyy'=1+x^2+y^2+x^2y^2 sinx(e^y + 1)dx=e^y(1+cosx)dy, Y(0)=0
At 2:00 pm a car's speedometer reads 30 mi/h. At 2:10 pm it reads 50 mi/h. Use the mean value theorem to show that at some time between 2:00 and 2:10 the acceleration is exactly 120 mi/h^2. Please show line by line work and be as clear as possible.